Generalized Fourier transform and its applications
The author studies the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space; the kernel of this operator is an entire vector function. Such transforms and their kernels are studied in detail. First of all, the author gives a definition of this operator and establishes its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. Necessary and sufficient conditions for the coincidence are obtained. The results are illustrated by examples of specific function spaces. Finally, the results are used to find the orders and types of operators on locally convex spaces.
scientific article; zbMATH DE number 5155481